In this paper, we study covert communications in a hybrid decode-and-forward (DF)/ amplify-and-forward (AF) relay system. The considered relay in normal operation forwards messages from a source node to a destination node in either DF or AF mode on request. Meanwhile, the source and destination nodes also attempt to secretly exchange covert messages such as confidential or sensitive information and avoid detection by the covert message detector embedded on the relay. We first establish an optimal DF/AF mode selection criterion to maximize the covert rate based on the analyses of delay-aware achievable covert rates of individual DF and AF modes. To further reduce the time complexity, we propose a low-complexity selection criterion as well for practical use. The numerical results demonstrate the covert rate gain as high as 50% and running time gain as high as 20% for particular system parameters, which verify the effectiveness of the proposed criteria.
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